Low for omega and equivalence class isomorphism properties

NERDS: New England Recursion & Definability SeminarSaturday, October 18, 20142:40 pmAssumption College, Worcester, MA

Jacob Suggs

Low for omega and equivalence class isomorphism properties

University of Connecticut

We look at the property of being low for isomorphism, restricted to certain classes of structures – if C is a class of structures, a set D is low for C isomorphism iff for any two structures in C, if D computes an isomorphism between them then there is a computable isomorphism between them. In particular we will show that exactly those sets which cannot compute non-zero Δ2 degrees are low for ω-isomorphism (when ω is viewed purely as an order), and we will show that no set which computes a non-zero Δ2 set or which computes a separating set for any two computably inseparable c.e. degrees is low for equivalence class isomorphism.

Jacob Suggs is a graduate student in computability theory at the University of Connecticut, working with Reed Solomon.

Posted by on September 16th, 2014